Some problems inspired by two-dimensional quantum gravity

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1992

OSTI ID:5578449

Apfeldorf, K M

This study addresses two problems inspired by two-dimensional quantum gravity, one stemming from the latticized approach and the other arising from the continuum approach. The discretized approach to random surfaces is employed, where matrix models describe two-dimensional gravity plus matter theories. The author shows equations describing the resulting theories of matter plus quantum gravity can be written compactly in terms of known functionals. These functions are the resolvents and the jets of the resolvents of q-th order differential operators. There are subsets of these functionals that form infinite involutive sets and are none other than the generalized Gel'fand Dikii potentials associated with the generalized Korteweg-de Vries hirarchies. The advantage of this work is that actions and string equations take on much simpler, uncomplicated forms and may be written out explicitly in all cases, including the interpolating or massive case. The author addresses the question of the connections between affine algebras and extend Virasoro algebras. It has been established that particular quantum hamiltonian reductions of sl(n) Well-Zumino-Novikov-Witten models constrained in conformally invariant ways give rise to the W[sup (l)][sub n] algebras. Performing quantum hamiltonian reduction by means of Drinfel'd Sokolov reduction for co-adjoint orbits, The author provides a complete description of all possible reductions of sl(3) current algebra, and also comment on the reduction of sl(4) current algebra. In the case of affine sl(3), It is shown that new reductions yield a family of twisted W[sub 3][sup (2)] algebras, as well as some other simpler algebras. Families of twisted W[sub n][sup (l)] algebras arising via quantum hamiltonian reductions are expected to occur in the sl(n) case as well.

• Research Organization: California Univ., Berkeley, CA (United States)
• OSTI ID: 5578449
• Country of Publication: United States
• Language: English

Related Subjects

661310* -- Relativity & Gravitation-- (1992-)
662110 -- General Theory of Particles & Fields-- Theory of Fields & Strings-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CURRENT ALGEBRA
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD THEORIES
FUNCTIONALS
FUNCTIONS
KORTEWEG-DE VRIES EQUATION
MATHEMATICAL MODELS
MATRICES
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
QUANTUM GRAVITY
QUANTUM MECHANICS
TWO-DIMENSIONAL CALCULATIONS